Spatial search on cayley graphs

In this work, I study the spatial search problem on direct products of cycle and complete graphs by continuous time quantum walks. I first show that search process on these networks is not generally efficient because of having highly degenerate eigenvalue spectra. Then, I enhance this process by considering the tranmission rate of the walk as a tunable parameter and find that for a special range of this parameter; the efficiency will be very high. Also, I investigate the impact of adding or removing a single edge on these networks and observe the faster search process.